Message #3572

From: ozaru_yafoo@yahoo.co.uk
Subject: Newbie queries on Magic Tile - Klein Rubik
Date: Fri, 25 Nov 2016 18:10:54 -0800

Hello everyone,

New member here - a first generation cuber (1981 UK championship) revisiting Rubiks 35 years on.

Somewhat randomly I found my way to http://roice3.org/magictile/mathologer/ http://roice3.org/magictile/mathologer/, downloaded MagicTile and have played a little with the Klein Bottle Rubik, recording a few simple macros (3-cycles, 2-flips etc.).

I’m slightly confused by a few aspects, and haven’t found much info on them (yet; my time is limited), including brief searches of this mailing list’s archive. So apologies for some rather verbose newbie questions.

1) Whereas on the original cube one expects a macro to do the same every time, I’m finding that the effects vary hugely, depending where I click when applying the macro (even within the same ‘facelet’). For example, an 8-move pure 3-cycle of corners, when clicked 1 mm away on the same facelet, mutates into a 3-cycle of edges plus two sets of twisted corner-swaps… Yet when I manually repeat the specific 8 moves I did, the results are as expected, a pure 3-cycle. Consequently, macros seem unusable (and there’s little incentive to try to solve the puzzle manually).

I did read the advice "It is important where you click when defining and executing the macro. You’ll achieve the best results if you click near tile vertices. Those are the ‘snap-to’ points when repositioning macros during execution." I’ve also seen the bug report at https://github.com/roice3/MagicTile/issues/13 https://github.com/roice3/MagicTile/issues/13. Yet I don’t see why this is an issue in such a simple model as this. If, for example, I click *anywhere* on the white facelet of the white-green-blue cubie and record e.g. Green CCW Purple CCW Green CW White CCW Green CCW Purple CW Green CW White CW [sorry if there is some better notation; it’s equivalent to R’D’RU’R’DRU on the cube], then I would expect that to replay the same way any time I clicked on any corner facelet. Can someone explain why it doesn’t? I’m guessing it’s because the app tries to adopt a single approach, and there are more complex models where it’s harder to define e.g. what "Purple CCW" really means with respect to the w-g-b [etc.] cubie initially clicked.

2) Some combinations on the Klein Bottle Rubik end up e.g. in a single corner twist, implying parity is not preserved in the way I’d expect (I did see one comment, which may be irrelevant, saying "a shift of the whole puzzle does change the parity"). Any simple explanation for why this is so? (I do understand how in the Klein bottle some cubies may appear to become ‘inside-out’, i.e. with facelets swapped, if they migrate to the other side of their original face, but can’t tell if that affects overall parity.)

3) A third question, largely unrelated. As I commented at https://www.youtube.com/watch?v=yhPH1369OWc&lc=z13jcrairmymxtzcd22miteospnthj5ak04 https://www.youtube.com/watch?v=yhPH1369OWc&lc=z13jcrairmymxtzcd22miteospnthj5ak04, I find it surprising that nobody (AFAIK) has yet produced a working 3D representation of a twistable 4D cube (equivalent to the 2D onscreen representations of 3D/4D/… cubes & other puzzles). Eli Reid responded there that "the most challenging part of solving a twisty puzzle is developing the sequences of moves you need to solve it, not executing those sequences" but most speedcubers would disagree, and some hobby cubers too enjoy the execution/exploration as much as simple sequencing. I know 3D models of hypercubes exist, but none appear to be movable. It may not be possible to produce a physically movable 3D representation of a 4D cube (just as I don’t think there are any physically movable 2D representations of 3D cubes, merely onscreen versions), but I still think it should be possible to create e.g. an expanded 3D cube with sensors/projectors/VR headsets etc. which make it possible to manipulate a 4D cube more easily than via mouse clicks. Any comments?

Many thanks in anticipation.

Ben Jones
ozaru.net